Geometry

Quantitative Aptitude (CGL)

Title

45:30

8 of 24 completed

5 of 15 completed

38 of 100 completed

8 of 20 completed

Indian Economy - Understanding the basics of Indian economic system

In a circle, a 14 cm long chord is at 24 cm from the centre of the circle. Find the length of the radius of the circle.

This questions was previously asked in

Combined Graduate Level Examination Tier I 2023

30 cm

25 cm

50 cm

27 cm

- Consider a chord of length 14 cm, which is 24 cm away from the center of the circle.

- Use the perpendicular bisector of the chord, which is the shortest distance from the center to the chord.

- The perpendicular bisector divides the chord into two equal parts: 7 cm each.

- Visualize a right triangle with:

- One leg being the distance from the center to the chord (24 cm).

- The other leg being half of the chord (7 cm).

- The hypotenuse being the radius of the circle (r).

- Apply the Pythagorean theorem: \( r^2 = 24^2 + 7^2 \).

- Calculate: \( r^2 = 576 + 49 = 625 \).

- Therefore, \( r = \sqrt{625} = 25 \) cm.

- Correct Answer: 25 cm